Our goals are to develop methods for statistical analyses of DNA sequence data and to understand the mechanisms of DNA evolution. The specific aims are: l. To examine current methods and develop new methods for estimating evolutionary dates, which is now a central issue in molecular evolution. We shall use the new methods to study divergence dates in mammals, which have recently become very controversial. 2. To develop methods for estimating selection intensities in different regions of a gene and to carry out statistical analyses of DNA sequence data from mammals. 3. To develop fast algorithms for finding optimal trees for the following methods: maximum likelihood, maximum parsimony, and minimum evolution. Such algorithms are much needed because these methods require a tremendous amount of computer time-and are not feasible for large trees. 4. An expert system for choosing the best tree reconstruction method for a data set according to the attributes of the data. 5. To introduce the neural network approach into phylogenetic study; this approach has proved extremely powerful in many branches of science and engineering.